{
  "id": "1810.10240",
  "version": "v1",
  "published": "2018-10-24T08:23:41.000Z",
  "updated": "2018-10-24T08:23:41.000Z",
  "title": "Negative curvature in automorphism groups of one-ended hyperbolic groups",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "14 pages. Comments are welcome",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "In this article, we show that some negative curvature may survive when taking the automorphism group of a finitely generated group. More precisely, we prove that the automorphism group $\\mathrm{Aut}(G)$ of a one-ended hyperbolic group $G$ which is not virtually a surface group turns out to be acylindrically hyperbolic. As a consequence, given an automorphism $\\varphi \\in \\mathrm{Aut}(G)$, we deduce that the semidirect product $G \\rtimes_\\varphi \\mathbb{Z}$ is acylindrically hyperbolic if and only if $\\varphi$ has infinite order in $\\mathrm{Out}(G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-24T08:23:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20E36",
      "20E08"
    ],
    "keywords": [
      "one-ended hyperbolic group",
      "automorphism group",
      "negative curvature",
      "acylindrically hyperbolic",
      "surface group turns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}